Wave Instrumental

[Dot Liljenquist]

Wavereanalysis databases (WRDBs) offer important advantages for the statistical characterization of wave climate (continuous time series, good spatial coverage, constant time span, homogeneous forcing, and more than a 40-yr-long time series) and for this reason, they have become a powerful tool for the design of offshore and coastal structures. However, WRDBs are not quantitatively perfect and corrections using instrumental observations must be addressed before they are used; this process is called calibration. The calibration is especially relevant near the coast and in areas where the orography is complex, since in these places the inaccuracy of WRDB is evident because of the bad description of the wind fields (i.e., insufficient forcing resolution). The quantitative differences between numerical and instrumental data suggest that different corrections should be applied depending on the mean direction of the sea state. This paper proposes a calibration method based on a nonlinear regression problem, where the corresponding correction parameters vary smoothly along the possible wave directions by means of cubic splines. The correction of significant wave height is performed using instrumental data: (i) buoy records and/or (ii) satellite data. The performance of the method is illustrated considering data from different locations around Spain.

Over the last few years, the development of wave reanalysis models has allowed for a detailed description of the wave climate in locations where long-term buoy records are not available. For this reason, they have become a powerful tool used for the design of offshore and coastal structures, since they provide long continuous time series records with good spatial coverage. However, reanalysis models are simplifications of reality that also use discrete forcing fields consisting of surface winds at different times, and quantitative results present differences when compared with recent instrumental data [buoys and/or satellite; see Caires and Sterl (2005); Cavaleri and Sclavo (2006)]. Cavaleri and Bertotti (2004) pointed out that when the orography is complex, the reanalysis inaccuracy becomes more evident because of the bad description of wind fields, which does not have the appropriate spatial and temporal resolution.The definition of the wave climate is crucial for coastal management and design, and there has been an increased interest in collecting information through instrumental devices, mainly using buoys and satellite altimetry. Buoys provide time series records of different ocean climate variables such as significant wave height, wave direction, wave period, currents, wind direction, etc., depending on the type of device. This information is very valuable for coastal design, however, it is only valid for the buoy location and in most cases the time series have interruptions due to disruptions on the normal use caused by buoy failure. Since the 1970s, several satellite missions [Skylab, the Goddard Earth Observing System-3 (GEOS-3), Seasat, Geosat, the Ocean Topography Experiment (TOPEX)/Poseidon, the European Remote Sensing Satellite-1 and -2 (ERS-1 and ERS-2), Geosat Follow-On (GFO), Jason-1, the Environmental Satellite (Envisat), and Jason-2] incorporate altimetry sensors that allow for the evaluation of different ocean climate variables, such as significant wave height with a high level of precision (3 cm; Krogstad and Barstow 1999). Altimetry data consist of information about significant wave height, among others variables, at different locations and time frames. However, with these two sources of information: buoys and altimetry, we do not have a temporal and spatial homogeneous record of ocean wave climate variables for design purposes. This reason has motivated an increased interest in the development of different wave generation models such as the Wave Ocean Model (WAM; see the WAMDI Group 1988), which using wind fields as input data, try to reproduce the evolution of wave generation and propagation on an homogeneous framework, both in time and space. These wind wave numerical databases provide continuous records of significant wave height, mean period, and mean direction, which are the key parameters for wave climate characterization, on a regular time basis (hourly or 3-hourly) over a defined grid. This information set has the advantages of both buoy and altimetry data (i.e., homogeneous spatial and temporal characteristics); however, as it has been pointed out by several authors, results are subject to bias with respect to instrumental data. Cavaleri and Sclavo (2006) summarized the main characteristics of these sources of information as follows:

As a result of the characteristics of reanalysis models, which are primarily fed using wind data, it is known that inaccuracies of wave reanalysis databases (WRDB) are mostly dependent on the bad description of the wind fields (see Feng et al. 2006), that is, insufficient forcing resolution. In coastal areas, there are additional factors that contribute to poor model performance such as inappropriate shallow-water physics in wave models, unresolved island blocking, imperfect bathymetry, etc. (see Cavaleri et al. 2007 for a summary). The quantitative differences between numerical and instrumental data suggests that different corrections should be applied depending on the mean direction of the sea state (i.e., for directions where the wind resolution is not enough to capture the local wind wave generation, but not for swell waves generated in areas where the wind resolution is sufficient to reproduce the wave dynamics). Toms (2009) proposes a calibration method where the parameters depend on the wave direction using harmonic functions. Mackay et al. (2010a,b) also point out the necessity of hindcast calibration in the context of wind energy resource assessment.

Corrections are made on empirical quantile information on a Gumbel probability paper scale. This allows to give more weight on the calibration procedure to the maximum data, which is more important from the design point of view.

Classic regression theory is applied to the calculation of the confidence intervals for parameters estimates and corrected values, giving an idea of the uncertainty associated with the calibration process.

The paper is organized as follows. In section 2, we present the nonlinear regression problem to be used for calibration purposes, analyzing in detail how the parameters are modeled via spline functions and it describes the complete calibration methodology including the diagnostic analysis and uncertainty characterization. Section 3 illustrates the functioning of the method through several examples on different locations around Spain, and in section 4 the effect of directional uncertainty on those locations is analyzed. Finally, in section 5 relevant conclusions are duly drawn.

In the previous section the nonlinear model proposed for parameter estimation of the calibration method was presented. However, the calibration procedure as a whole (i.e., the obtention of the final calibrated time series in a particular location) involves several additional steps:

Data and quantile selection: The calibration procedure is intended to correct the probability distribution function of the reanalysis variable in order to be as close as possible to the instrumental variable probability distribution. For this task, it is required to use both reanalysis and instrumental data coincident in time and space, and for the selection of the appropriate quantiles to be compared.

Diagnostic time series analysis calibration: Using also standard regression techniques, confidence intervals for the calibrated times series are calculated. This diagnostic allows quantifying the uncertainty associated with the calibration procedure. Several diagnostic plots are also listed.

The target of the calibration procedure is to correct the significant wave height reanalysis time series record at a particular location (see the objective point in Fig. 2) using instrumental data. For this purpose, the first step of the method is to select nd data pairs in an area close to the objective point where the wave climate is similar. The definition of an automatic criterion to select the data to be incorporated for the posterior parameter estimation procedure is difficult; however, we propose a procedure based on vector correlation (Crosby et al. 2003), sensitivity tests (Toms 2009), and designer criterion. The guidelines for data selection are summarized as follows:

Select a circular area around the objective point of radius r (neighborhood criterion). The length of the radius depends on the ocean climate homogeneity and the number of available data. There must be a compromise between the data record length and its homogeneity, since the longer the radius the higher the length of the record, but it is more likely to use data with different wave climate. In our experience and after several sensitivity tests using different parameter configurations around the Spanish coast, we derived the following rule of thumb: (i) r = 0.5 for complex areas such as Mediterranean Sea; (ii) r = 1 for Atlantic Ocean coastlines, and (iii) r = 2 for open areas.

3a8082e126